If there was ONE privately run exam board, they'd have a monopoly - bad for costs, and for service, they could run a **** service and all the schools would still have to buy in, or set prices high, and schools would HAVE to buy in?
Plus, it means if they made a mistake, it affects FAR more people
*EDIT*
But I do agree, I ****ing hate exam boards, and their lack of communication, their ****ty marking, their crap paper and comments turn around times, their high costs, ESPECIALLY, AQA!